help for algebraic structures 2

help for algebraic structures 2

Define the set M and the binary operation â—¦ in the following way:

M = x ; x ∈ R(real number), x not equal to 1/5 , a â—¦ b = a + b + 5a · b

where + and · denote the usual addition and multiplication in R. Show that (M, â—¦) is a group. Determine whether this group is Abelian.

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